Level-of-detail eigenvector determination in a graphics environment

A method comprising:

• identifying, by a rasterizer hardware unit of a processing core, components of partial derivative vectors corresponding to two adjacent lines of a quadrilateral in texture space of an image, the quadrilateral corresponding to a pixel sampling area in screen space;
• combining the partial derivative vectors into a transformation matrix representing a transformation of coordinates from the screen space to the texture space, wherein the transformation produces an ellipse in the texture space when applied to a unit circle in the screen space;
• determining a value of a square of a major axis length (major squared) of the ellipse based on a sum of squares (SOS) of the components of the transformation matrix and a determinant of the transformation matrix;
• and
• computing eigenvector values for the ellipse using the components of the partial derivative vectors, the determinant of the transformation matrix, and the value of the major squared.

A non-transitory computer-readable storage medium having stored thereon executable computer program instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising:

• identifying, by a rasterizer hardware unit of the one or more processors, components of partial derivative vectors corresponding to two adjacent lines of a quadrilateral in texture space of an image, the quadrilateral corresponding to a pixel sampling area in screen space;
• combining the partial derivative vectors into a transformation matrix representing a transformation of coordinates from the screen space to the texture space, wherein the transformation produces an ellipse in the texture space when applied to a unit circle in the screen space;
• determining a value of a square of a major axis length (major squared) of the ellipse based on a sum of squares (SOS) of the components of the transformation matrix and a determinant of the transformation matrix;
• and
• computing eigenvector values for the ellipse using the components of the partial derivative vectors, the determinant of the transformation matrix, and the value of the major squared.